LMFDB - Embedded newform 128.3.h.a.111.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,3,Mod(15,128)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 1]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("128.15");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	128.h (of order $8$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.48774738381$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			111.3
Character	$\chi$	$=$	128.111
Dual form			128.3.h.a.15.3

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.58190 - 0.655246i) q^{3} +(4.18866 - 1.73500i) q^{5} +(-3.93197 - 3.93197i) q^{7} +(-4.29089 - 4.29089i) q^{9} +O(q^{10})$	\(q+(-1.58190 - 0.655246i) q^{3} +(4.18866 - 1.73500i) q^{5} +(-3.93197 - 3.93197i) q^{7} +(-4.29089 - 4.29089i) q^{9} +(14.2355 - 5.89652i) q^{11} +(0.454935 + 0.188440i) q^{13} -7.76291 q^{15} -26.5635i q^{17} +(7.25040 - 17.5040i) q^{19} +(3.64359 + 8.79641i) q^{21} +(-0.775848 + 0.775848i) q^{23} +(-3.14303 + 3.14303i) q^{25} +(9.87340 + 23.8365i) q^{27} +(-17.9907 + 43.4334i) q^{29} +39.6852i q^{31} -26.3828 q^{33} +(-23.2916 - 9.64771i) q^{35} +(36.4715 - 15.1070i) q^{37} +(-0.596189 - 0.596189i) q^{39} +(38.9661 + 38.9661i) q^{41} +(14.2899 - 5.91907i) q^{43} +(-25.4177 - 10.5284i) q^{45} -62.1759 q^{47} -18.0792i q^{49} +(-17.4057 + 42.0210i) q^{51} +(11.4986 + 27.7600i) q^{53} +(49.3970 - 49.3970i) q^{55} +(-22.9389 + 22.9389i) q^{57} +(5.30584 + 12.8094i) q^{59} +(14.1407 - 34.1386i) q^{61} +33.7433i q^{63} +2.23251 q^{65} +(-26.1257 - 10.8216i) q^{67} +(1.73569 - 0.718946i) q^{69} +(-17.7859 - 17.7859i) q^{71} +(12.8313 + 12.8313i) q^{73} +(7.03144 - 2.91252i) q^{75} +(-79.1584 - 32.7885i) q^{77} +144.157 q^{79} +10.4375i q^{81} +(10.9897 - 26.5314i) q^{83} +(-46.0877 - 111.266i) q^{85} +(56.9192 - 56.9192i) q^{87} +(-5.92267 + 5.92267i) q^{89} +(-1.04785 - 2.52973i) q^{91} +(26.0036 - 62.7782i) q^{93} -85.8978i q^{95} +66.9192 q^{97} +(-86.3841 - 35.7815i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 28 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9	$ 28 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + 4 q^{11} - 4 q^{13} + 8 q^{15} + 4 q^{19} - 4 q^{21} + 68 q^{23} - 4 q^{25} + 100 q^{27} - 4 q^{29} - 8 q^{33} - 92 q^{35} - 4 q^{37} - 188 q^{39} - 4 q^{41} - 92 q^{43} - 40 q^{45} + 8 q^{47} - 224 q^{51} - 164 q^{53} - 252 q^{55} - 4 q^{57} - 124 q^{59} - 68 q^{61} - 8 q^{65} + 164 q^{67} + 188 q^{69} + 260 q^{71} - 4 q^{73} + 488 q^{75} + 220 q^{77} + 520 q^{79} + 484 q^{83} + 96 q^{85} + 452 q^{87} - 4 q^{89} + 196 q^{91} + 32 q^{93} - 8 q^{97} - 216 q^{99}+O(q^{100}) $ 28 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9 + 4 * q^11 - 4 * q^13 + 8 * q^15 + 4 * q^19 - 4 * q^21 + 68 * q^23 - 4 * q^25 + 100 * q^27 - 4 * q^29 - 8 * q^33 - 92 * q^35 - 4 * q^37 - 188 * q^39 - 4 * q^41 - 92 * q^43 - 40 * q^45 + 8 * q^47 - 224 * q^51 - 164 * q^53 - 252 * q^55 - 4 * q^57 - 124 * q^59 - 68 * q^61 - 8 * q^65 + 164 * q^67 + 188 * q^69 + 260 * q^71 - 4 * q^73 + 488 * q^75 + 220 * q^77 + 520 * q^79 + 484 * q^83 + 96 * q^85 + 452 * q^87 - 4 * q^89 + 196 * q^91 + 32 * q^93 - 8 * q^97 - 216 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.58190	−	0.655246i	−0.527302	−	0.218415i	0.103119	−	0.994669i	$-0.467118\pi$
$3$	−1.58190	−	0.655246i	−0.527302	−	0.218415i	−0.630421	+	0.776254i	$0.717118\pi$
$4$		0			0
$5$	4.18866	−	1.73500i	0.837732	−	0.347000i	0.0777729	−	0.996971i	$-0.475219\pi$
$5$	4.18866	−	1.73500i	0.837732	−	0.347000i	0.759959	+	0.649971i	$0.225219\pi$
$6$		0			0
$7$	−3.93197	−	3.93197i	−0.561710	−	0.561710i	0.368083	−	0.929793i	$-0.380014\pi$
$7$	−3.93197	−	3.93197i	−0.561710	−	0.561710i	−0.929793	+	0.368083i	$0.880014\pi$
$8$		0			0
$9$	−4.29089	−	4.29089i	−0.476765	−	0.476765i
$10$		0			0
$11$	14.2355	−	5.89652i	1.29413	−	0.536048i	0.373919	−	0.927462i	$-0.378014\pi$
$11$	14.2355	−	5.89652i	1.29413	−	0.536048i	0.920215	+	0.391414i	$0.128014\pi$
$12$		0			0
$13$	0.454935	+	0.188440i	0.0349950	+	0.0144954i	0.400112	−	0.916466i	$-0.368971\pi$
$13$	0.454935	+	0.188440i	0.0349950	+	0.0144954i	−0.365117	+	0.930962i	$0.618971\pi$
$14$		0			0
$15$	−7.76291			−0.517527
$16$		0			0
$17$		−	26.5635i		−	1.56256i	−0.624181	−	0.781280i	$-0.714567\pi$
$17$		−	26.5635i		−	1.56256i	0.624181	−	0.781280i	$-0.285433\pi$
$18$		0			0
$19$	7.25040	−	17.5040i	0.381600	−	0.921264i	−0.610057	−	0.792358i	$-0.708853\pi$
$19$	7.25040	−	17.5040i	0.381600	−	0.921264i	0.991657	−	0.128906i	$-0.0411466\pi$
$20$		0			0
$21$	3.64359	+	8.79641i	0.173504	+	0.418877i
$22$		0			0
$23$	−0.775848	+	0.775848i	−0.0337325	+	0.0337325i	−0.723772	−	0.690039i	$-0.757593\pi$
$23$	−0.775848	+	0.775848i	−0.0337325	+	0.0337325i	0.690039	+	0.723772i	$0.257593\pi$
$24$		0			0
$25$	−3.14303	+	3.14303i	−0.125721	+	0.125721i
$26$		0			0
$27$	9.87340	+	23.8365i	0.365682	+	0.882833i
$28$		0			0
$29$	−17.9907	+	43.4334i	−0.620369	+	1.49770i	0.230901	+	0.972977i	$0.425833\pi$
$29$	−17.9907	+	43.4334i	−0.620369	+	1.49770i	−0.851271	+	0.524727i	$0.824167\pi$
$30$		0			0
$31$			39.6852i			1.28017i	0.768306	+	0.640083i	$0.221100\pi$
$31$			39.6852i			1.28017i	−0.768306	+	0.640083i	$0.778900\pi$
$32$		0			0
$33$	−26.3828			−0.799480
$34$		0			0
$35$	−23.2916	−	9.64771i	−0.665475	−	0.275649i
$36$		0			0
$37$	36.4715	−	15.1070i	0.985717	−	0.408297i	0.169177	−	0.985586i	$-0.445889\pi$
$37$	36.4715	−	15.1070i	0.985717	−	0.408297i	0.816540	+	0.577288i	$0.195889\pi$
$38$		0			0
$39$	−0.596189	−	0.596189i	−0.0152869	−	0.0152869i
$40$		0			0
$41$	38.9661	+	38.9661i	0.950392	+	0.950392i	0.998826	−	0.0484342i	$-0.0154231\pi$
$41$	38.9661	+	38.9661i	0.950392	+	0.950392i	−0.0484342	+	0.998826i	$0.515423\pi$
$42$		0			0
$43$	14.2899	−	5.91907i	0.332324	−	0.137653i	−0.210282	−	0.977641i	$-0.567438\pi$
$43$	14.2899	−	5.91907i	0.332324	−	0.137653i	0.542605	+	0.839988i	$0.317438\pi$
$44$		0			0
$45$	−25.4177	−	10.5284i	−0.564839	−	0.233964i
$46$		0			0
$47$	−62.1759			−1.32289			−0.661446	−	0.749993i	$-0.730057\pi$
$47$	−62.1759			−1.32289			−0.661446	+	0.749993i	$0.730057\pi$
$48$		0			0
$49$		−	18.0792i		−	0.368964i
$50$		0			0
$51$	−17.4057	+	42.0210i	−0.341287	+	0.823940i
$52$		0			0
$53$	11.4986	+	27.7600i	0.216954	+	0.523773i	0.994462	−	0.105100i	$-0.0335163\pi$
$53$	11.4986	+	27.7600i	0.216954	+	0.523773i	−0.777508	+	0.628874i	$0.783516\pi$
$54$		0			0
$55$	49.3970	−	49.3970i	0.898128	−	0.898128i
$56$		0			0
$57$	−22.9389	+	22.9389i	−0.402437	+	0.402437i
$58$		0			0
$59$	5.30584	+	12.8094i	0.0899295	+	0.217109i	0.962445	−	0.271478i	$-0.0875124\pi$
$59$	5.30584	+	12.8094i	0.0899295	+	0.217109i	−0.872515	+	0.488587i	$0.837512\pi$
$60$		0			0
$61$	14.1407	−	34.1386i	0.231814	−	0.559650i	−0.764576	−	0.644533i	$-0.777052\pi$
$61$	14.1407	−	34.1386i	0.231814	−	0.559650i	0.996391	+	0.0848835i	$0.0270518\pi$
$62$		0			0
$63$			33.7433i			0.535607i
$64$		0			0
$65$	2.23251			0.0343463
$66$		0			0
$67$	−26.1257	−	10.8216i	−0.389937	−	0.161517i	0.179097	−	0.983831i	$-0.442682\pi$
$67$	−26.1257	−	10.8216i	−0.389937	−	0.161517i	−0.569033	+	0.822314i	$0.692682\pi$
$68$		0			0
$69$	1.73569	−	0.718946i	0.0251549	−	0.0104195i
$70$		0			0
$71$	−17.7859	−	17.7859i	−0.250505	−	0.250505i	0.570672	−	0.821178i	$-0.306683\pi$
$71$	−17.7859	−	17.7859i	−0.250505	−	0.250505i	−0.821178	+	0.570672i	$0.806683\pi$
$72$		0			0
$73$	12.8313	+	12.8313i	0.175771	+	0.175771i	0.789510	−	0.613738i	$-0.210335\pi$
$73$	12.8313	+	12.8313i	0.175771	+	0.175771i	−0.613738	+	0.789510i	$0.710335\pi$
$74$		0			0
$75$	7.03144	−	2.91252i	0.0937525	−	0.0388336i
$76$		0			0
$77$	−79.1584	−	32.7885i	−1.02803	−	0.425824i
$78$		0			0
$79$	144.157			1.82477			0.912383	−	0.409337i	$-0.134240\pi$
$79$	144.157			1.82477			0.912383	+	0.409337i	$0.134240\pi$
$80$		0			0
$81$			10.4375i			0.128858i
$82$		0			0
$83$	10.9897	−	26.5314i	0.132406	−	0.319655i	−0.843747	−	0.536741i	$-0.819655\pi$
$83$	10.9897	−	26.5314i	0.132406	−	0.319655i	0.976153	+	0.217086i	$0.0696552\pi$
$84$		0			0
$85$	−46.0877	−	111.266i	−0.542208	−	1.30901i
$86$		0			0
$87$	56.9192	−	56.9192i	0.654244	−	0.654244i
$88$		0			0
$89$	−5.92267	+	5.92267i	−0.0665469	+	0.0665469i	−0.739597	−	0.673050i	$-0.764984\pi$
$89$	−5.92267	+	5.92267i	−0.0665469	+	0.0665469i	0.673050	+	0.739597i	$0.264984\pi$
$90$		0			0
$91$	−1.04785	−	2.52973i	−0.0115148	−	0.0277993i
$92$		0			0
$93$	26.0036	−	62.7782i	0.279608	−	0.675034i
$94$		0			0
$95$		−	85.8978i		−	0.904187i
$96$		0			0
$97$	66.9192			0.689889			0.344944	−	0.938623i	$-0.387898\pi$
$97$	66.9192			0.689889			0.344944	+	0.938623i	$0.387898\pi$
$98$		0			0
$99$	−86.3841	−	35.7815i	−0.872566	−	0.361429i
$100$		0			0
$101$	23.3697	−	9.68007i	0.231384	−	0.0958422i	−0.263979	−	0.964528i	$-0.585035\pi$
$101$	23.3697	−	9.68007i	0.231384	−	0.0958422i	0.495363	+	0.868686i	$0.335035\pi$
$102$		0			0
$103$	15.5454	+	15.5454i	0.150927	+	0.150927i	0.778532	−	0.627605i	$-0.215965\pi$
$103$	15.5454	+	15.5454i	0.150927	+	0.150927i	−0.627605	+	0.778532i	$0.715965\pi$
$104$		0			0
$105$	30.5235	+	30.5235i	0.290700	+	0.290700i
$106$		0			0
$107$	−107.060	+	44.3456i	−1.00056	+	0.414444i	−0.822001	−	0.569485i	$-0.807143\pi$
$107$	−107.060	+	44.3456i	−1.00056	+	0.414444i	−0.178556	+	0.983930i	$0.557143\pi$
$108$		0			0
$109$	82.3132	+	34.0952i	0.755167	+	0.312800i	0.726848	−	0.686799i	$-0.240985\pi$
$109$	82.3132	+	34.0952i	0.755167	+	0.312800i	0.0283190	+	0.999599i	$0.490985\pi$
$110$		0			0
$111$	−67.5933			−0.608949
$112$		0			0
$113$			9.91566i			0.0877492i	0.999037	+	0.0438746i	$0.0139702\pi$
$113$			9.91566i			0.0877492i	−0.999037	+	0.0438746i	$0.986030\pi$
$114$		0			0
$115$	−1.90367	+	4.59586i	−0.0165536	+	0.0399640i
$116$		0			0
$117$	−1.14350	−	2.76065i	−0.00977350	−	0.0235953i
$118$		0			0
$119$	−104.447	+	104.447i	−0.877705	+	0.877705i
$120$		0			0
$121$	82.3196	−	82.3196i	0.680327	−	0.680327i
$122$		0			0
$123$	−36.1082	−	87.1730i	−0.293563	−	0.708724i
$124$		0			0
$125$	−51.0869	+	123.335i	−0.408695	+	0.986678i
$126$		0			0
$127$		−	59.4093i		−	0.467790i	−0.972262	−	0.233895i	$-0.924853\pi$
$127$		−	59.4093i		−	0.467790i	0.972262	−	0.233895i	$-0.0751471\pi$
$128$		0			0
$129$	−26.4837			−0.205300
$130$		0			0
$131$	176.426	+	73.0781i	1.34676	+	0.557848i	0.935390	−	0.353618i	$-0.115049\pi$
$131$	176.426	+	73.0781i	1.34676	+	0.557848i	0.411375	+	0.911466i	$0.365049\pi$
$132$		0			0
$133$	−97.3336	+	40.3169i	−0.731832	+	0.303135i
$134$		0			0
$135$	82.7126	+	82.7126i	0.612686	+	0.612686i
$136$		0			0
$137$	−138.710	−	138.710i	−1.01248	−	1.01248i	−0.999921	−	0.0125608i	$-0.996002\pi$
$137$	−138.710	−	138.710i	−1.01248	−	1.01248i	−0.0125608	−	0.999921i	$-0.503998\pi$
$138$		0			0
$139$	63.7662	−	26.4128i	0.458750	−	0.190020i	−0.141327	−	0.989963i	$-0.545137\pi$
$139$	63.7662	−	26.4128i	0.458750	−	0.190020i	0.600077	+	0.799943i	$0.295137\pi$
$140$		0			0
$141$	98.3563	+	40.7405i	0.697563	+	0.288940i
$142$		0			0
$143$	7.58736			0.0530584
$144$		0			0
$145$			213.142i			1.46994i
$146$		0			0
$147$	−11.8464	+	28.5996i	−0.0805874	+	0.194555i
$148$		0			0
$149$	41.3888	+	99.9214i	0.277777	+	0.670613i	0.999773	−	0.0212835i	$-0.00677526\pi$
$149$	41.3888	+	99.9214i	0.277777	+	0.670613i	−0.721996	+	0.691897i	$0.756775\pi$
$150$		0			0
$151$	−159.036	+	159.036i	−1.05322	+	1.05322i	−0.0547164	+	0.998502i	$0.517425\pi$
$151$	−159.036	+	159.036i	−1.05322	+	1.05322i	−0.998502	+	0.0547164i	$0.982575\pi$
$152$		0			0
$153$	−113.981	+	113.981i	−0.744974	+	0.744974i
$154$		0			0
$155$	68.8537	+	166.228i	0.444218	+	1.07244i
$156$		0			0
$157$	31.5775	−	76.2349i	0.201131	−	0.485573i	−0.790843	−	0.612020i	$-0.790357\pi$
$157$	31.5775	−	76.2349i	0.201131	−	0.485573i	0.991973	+	0.126447i	$0.0403573\pi$
$158$		0			0
$159$		−	51.4480i		−	0.323573i
$160$		0			0
$161$	6.10122			0.0378958
$162$		0			0
$163$	192.658	+	79.8016i	1.18195	+	0.489581i	0.885126	−	0.465351i	$-0.154072\pi$
$163$	192.658	+	79.8016i	1.18195	+	0.489581i	0.296826	+	0.954932i	$0.404072\pi$
$164$		0			0
$165$	−110.509	+	45.7742i	−0.669749	+	0.277419i
$166$		0			0
$167$	−76.7432	−	76.7432i	−0.459540	−	0.459540i	0.438964	−	0.898504i	$-0.355345\pi$
$167$	−76.7432	−	76.7432i	−0.459540	−	0.459540i	−0.898504	+	0.438964i	$0.855345\pi$
$168$		0			0
$169$	−119.330	−	119.330i	−0.706092	−	0.706092i
$170$		0			0
$171$	−106.218	+	43.9971i	−0.621160	+	0.257293i
$172$		0			0
$173$	46.0052	+	19.0560i	0.265926	+	0.110150i	0.511663	−	0.859187i	$-0.329030\pi$
$173$	46.0052	+	19.0560i	0.265926	+	0.110150i	−0.245737	+	0.969337i	$0.579030\pi$
$174$		0			0
$175$	24.7166			0.141238
$176$		0			0
$177$		−	23.7399i		−	0.134124i
$178$		0			0
$179$	29.4799	−	71.1707i	0.164692	−	0.397602i	−0.819891	−	0.572520i	$-0.805966\pi$
$179$	29.4799	−	71.1707i	0.164692	−	0.397602i	0.984583	+	0.174918i	$0.0559660\pi$
$180$		0			0
$181$	46.7381	+	112.836i	0.258222	+	0.623402i	0.998821	−	0.0485445i	$-0.0154583\pi$
$181$	46.7381	+	112.836i	0.258222	+	0.623402i	−0.740599	+	0.671947i	$0.765458\pi$
$182$		0			0
$183$	−44.7384	+	44.7384i	−0.244472	+	0.244472i
$184$		0			0
$185$	126.556	−	126.556i	0.684087	−	0.684087i
$186$		0			0
$187$	−156.632	−	378.144i	−0.837606	−	2.02216i
$188$		0			0
$189$	54.9025	−	132.546i	0.290489	−	0.701303i
$190$		0			0
$191$			227.376i			1.19045i	0.803559	+	0.595226i	$0.202937\pi$
$191$			227.376i			1.19045i	−0.803559	+	0.595226i	$0.797063\pi$
$192$		0			0
$193$	−46.4565			−0.240707			−0.120354	−	0.992731i	$-0.538403\pi$
$193$	−46.4565			−0.240707			−0.120354	+	0.992731i	$0.538403\pi$
$194$		0			0
$195$	−3.53162	−	1.46285i	−0.0181109	−	0.00750177i
$196$		0			0
$197$	−186.490	+	77.2467i	−0.946650	+	0.392115i	−0.801971	−	0.597363i	$-0.796215\pi$
$197$	−186.490	+	77.2467i	−0.946650	+	0.392115i	−0.144680	+	0.989479i	$0.546215\pi$
$198$		0			0
$199$	−54.5057	−	54.5057i	−0.273898	−	0.273898i	0.556769	−	0.830667i	$-0.312041\pi$
$199$	−54.5057	−	54.5057i	−0.273898	−	0.273898i	−0.830667	+	0.556769i	$0.812041\pi$
$200$		0			0
$201$	34.2376	+	34.2376i	0.170336	+	0.170336i
$202$		0			0
$203$	241.518	−	100.040i	1.18974	−	0.492808i
$204$		0			0
$205$	230.822	+	95.6095i	1.12596	+	0.466388i
$206$		0			0
$207$	6.65815			0.0321650
$208$		0			0
$209$		−	291.930i		−	1.39679i
$210$		0			0
$211$	−35.0586	+	84.6390i	−0.166155	+	0.401133i	−0.984923	−	0.172991i	$-0.944657\pi$
$211$	−35.0586	+	84.6390i	−0.166155	+	0.401133i	0.818769	+	0.574123i	$0.194657\pi$
$212$		0			0
$213$	16.4814	+	39.7897i	0.0773776	+	0.186806i
$214$		0			0
$215$	49.5860	−	49.5860i	0.230632	−	0.230632i
$216$		0			0
$217$	156.041	−	156.041i	0.719082	−	0.719082i
$218$		0			0
$219$	−11.8902	−	28.7056i	−0.0542933	−	0.131076i
$220$		0			0
$221$	5.00564	−	12.0847i	0.0226499	−	0.0546818i
$222$		0			0
$223$		−	428.136i		−	1.91989i	−0.280181	−	0.959947i	$-0.590394\pi$
$223$		−	428.136i		−	1.91989i	0.280181	−	0.959947i	$-0.409606\pi$
$224$		0			0
$225$	26.9728			0.119879
$226$		0			0
$227$	112.195	+	46.4728i	0.494252	+	0.204726i	0.615865	−	0.787852i	$-0.288807\pi$
$227$	112.195	+	46.4728i	0.494252	+	0.204726i	−0.121613	+	0.992578i	$0.538807\pi$
$228$		0			0
$229$	128.033	−	53.0331i	0.559097	−	0.231586i	−0.0851960	−	0.996364i	$-0.527152\pi$
$229$	128.033	−	53.0331i	0.559097	−	0.231586i	0.644293	+	0.764779i	$0.277152\pi$
$230$		0			0
$231$	103.736	+	103.736i	0.449076	+	0.449076i
$232$		0			0
$233$	−90.6042	−	90.6042i	−0.388859	−	0.388859i	0.485421	−	0.874280i	$-0.338666\pi$
$233$	−90.6042	−	90.6042i	−0.388859	−	0.388859i	−0.874280	+	0.485421i	$0.838666\pi$
$234$		0			0
$235$	−260.434	+	107.875i	−1.10823	+	0.459043i
$236$		0			0
$237$	−228.042	−	94.4581i	−0.962202	−	0.398557i
$238$		0			0
$239$	−283.775			−1.18734			−0.593672	−	0.804707i	$-0.702323\pi$
$239$	−283.775			−1.18734			−0.593672	+	0.804707i	$0.702323\pi$
$240$		0			0
$241$			309.483i			1.28416i	0.766636	+	0.642082i	$0.221929\pi$
$241$			309.483i			1.28416i	−0.766636	+	0.642082i	$0.778071\pi$
$242$		0			0
$243$	95.6997	−	231.040i	0.393826	−	0.950780i
$244$		0			0
$245$	−31.3674	−	75.7277i	−0.128030	−	0.309093i
$246$		0			0
$247$	6.59693	−	6.59693i	0.0267082	−	0.0267082i
$248$		0			0
$249$	−34.7692	+	34.7692i	−0.139635	+	0.139635i
$250$		0			0
$251$	33.9351	+	81.9265i	0.135199	+	0.326400i	0.976951	−	0.213465i	$-0.0684750\pi$
$251$	33.9351	+	81.9265i	0.135199	+	0.326400i	−0.841751	+	0.539866i	$0.818475\pi$
$252$		0			0
$253$	−6.46975	+	15.6194i	−0.0255721	+	0.0617366i
$254$		0			0
$255$			206.210i			0.808668i
$256$		0			0
$257$	193.069			0.751241			0.375621	−	0.926774i	$-0.377430\pi$
$257$	193.069			0.751241			0.375621	+	0.926774i	$0.377430\pi$
$258$		0			0
$259$	−202.805	−	84.0047i	−0.783032	−	0.324342i
$260$		0			0
$261$	263.564	−	109.172i	1.00982	−	0.418283i
$262$		0			0
$263$	14.4799	+	14.4799i	0.0550568	+	0.0550568i	0.734099	−	0.679042i	$-0.237605\pi$
$263$	14.4799	+	14.4799i	0.0550568	+	0.0550568i	−0.679042	+	0.734099i	$0.737605\pi$
$264$		0			0
$265$	96.3271	+	96.3271i	0.363498	+	0.363498i
$266$		0			0
$267$	13.2499	−	5.48830i	0.0496252	−	0.0205554i
$268$		0			0
$269$	−125.951	−	52.1707i	−0.468220	−	0.193943i	0.136083	−	0.990697i	$-0.456549\pi$
$269$	−125.951	−	52.1707i	−0.468220	−	0.193943i	−0.604303	+	0.796754i	$0.706549\pi$
$270$		0			0
$271$	490.650			1.81052			0.905258	−	0.424863i	$-0.139678\pi$
$271$	490.650			1.81052			0.905258	+	0.424863i	$0.139678\pi$
$272$		0			0
$273$			4.68840i			0.0171736i
$274$		0			0
$275$	−26.2096	+	63.2755i	−0.0953076	+	0.230093i
$276$		0			0
$277$	−183.667	−	443.412i	−0.663059	−	1.60076i	−0.792985	−	0.609241i	$-0.791474\pi$
$277$	−183.667	−	443.412i	−0.663059	−	1.60076i	0.129926	−	0.991524i	$-0.458526\pi$
$278$		0			0
$279$	170.285	−	170.285i	0.610339	−	0.610339i
$280$		0			0
$281$	−164.474	+	164.474i	−0.585316	+	0.585316i	−0.936359	−	0.351043i	$-0.885827\pi$
$281$	−164.474	+	164.474i	−0.585316	+	0.585316i	0.351043	+	0.936359i	$0.385827\pi$
$282$		0			0
$283$	98.6436	+	238.147i	0.348564	+	0.841508i	0.996790	+	0.0800601i	$0.0255112\pi$
$283$	98.6436	+	238.147i	0.348564	+	0.841508i	−0.648226	+	0.761448i	$0.724489\pi$
$284$		0			0
$285$	−56.2842	+	135.882i	−0.197488	+	0.476779i
$286$		0			0
$287$		−	306.427i		−	1.06769i
$288$		0			0
$289$	−416.621			−1.44159
$290$		0			0
$291$	−105.860	−	43.8486i	−0.363779	−	0.150682i
$292$		0			0
$293$	−60.5536	+	25.0821i	−0.206668	+	0.0856045i	−0.483616	−	0.875280i	$-0.660677\pi$
$293$	−60.5536	+	25.0821i	−0.206668	+	0.0856045i	0.276948	+	0.960885i	$0.410677\pi$
$294$		0			0
$295$	44.4487	+	44.4487i	0.150674	+	0.150674i
$296$		0			0
$297$	281.105	+	281.105i	0.946481	+	0.946481i
$298$		0			0
$299$	−0.499162	+	0.206759i	−0.00166944	+	0.000691503i
$300$		0			0
$301$	−79.4611	−	32.9139i	−0.263990	−	0.109348i
$302$		0			0
$303$	−43.3115			−0.142942
$304$		0			0
$305$		−	167.529i		−	0.549276i
$306$		0			0
$307$	−166.166	+	401.160i	−0.541257	+	1.30671i	0.382580	+	0.923923i	$0.375036\pi$
$307$	−166.166	+	401.160i	−0.541257	+	1.30671i	−0.923836	+	0.382787i	$0.874964\pi$
$308$		0			0
$309$	−14.4053	−	34.7775i	−0.0466191	−	0.112548i
$310$		0			0
$311$	261.640	−	261.640i	0.841288	−	0.841288i	−0.147739	−	0.989026i	$-0.547199\pi$
$311$	261.640	−	261.640i	0.841288	−	0.841288i	0.989026	+	0.147739i	$0.0471995\pi$
$312$		0			0
$313$	−301.723	+	301.723i	−0.963972	+	0.963972i	−0.999373	−	0.0354015i	$-0.988729\pi$
$313$	−301.723	+	301.723i	−0.963972	+	0.963972i	0.0354015	+	0.999373i	$0.488729\pi$
$314$		0			0
$315$	58.5445	+	141.339i	0.185856	+	0.448695i
$316$		0			0
$317$	11.4511	−	27.6454i	0.0361233	−	0.0872094i	−0.904788	−	0.425862i	$-0.859971\pi$
$317$	11.4511	−	27.6454i	0.0361233	−	0.0872094i	0.940912	+	0.338652i	$0.109971\pi$
$318$		0			0
$319$			724.378i			2.27078i
$320$		0			0
$321$	198.415			0.618117
$322$		0			0
$323$	−464.968	−	192.596i	−1.43953	−	0.596273i
$324$		0			0
$325$	−2.02215	+	0.837602i	−0.00622200	+	0.00257724i
$326$		0			0
$327$	−107.871	−	107.871i	−0.329880	−	0.329880i
$328$		0			0
$329$	244.474	+	244.474i	0.743081	+	0.743081i
$330$		0			0
$331$	117.333	−	48.6009i	0.354480	−	0.146830i	−0.198335	−	0.980134i	$-0.563553\pi$
$331$	117.333	−	48.6009i	0.354480	−	0.146830i	0.552815	+	0.833304i	$0.313553\pi$
$332$		0			0
$333$	−221.318	−	91.6728i	−0.664617	−	0.275294i
$334$		0			0
$335$	−128.207			−0.382709
$336$		0			0
$337$			148.325i			0.440134i	0.975485	+	0.220067i	$0.0706276\pi$
$337$			148.325i			0.440134i	−0.975485	+	0.220067i	$0.929372\pi$
$338$		0			0
$339$	6.49720	−	15.6856i	0.0191658	−	0.0462703i
$340$		0			0
$341$	234.004	+	564.937i	0.686230	+	1.65671i
$342$		0			0
$343$	−263.753	+	263.753i	−0.768961	+	0.768961i
$344$		0			0
$345$	6.02284	−	6.02284i	0.0174575	−	0.0174575i
$346$		0			0
$347$	215.625	+	520.565i	0.621398	+	1.50019i	0.850062	+	0.526682i	$0.176564\pi$
$347$	215.625	+	520.565i	0.621398	+	1.50019i	−0.228664	+	0.973505i	$0.573436\pi$
$348$		0			0
$349$	−92.9006	+	224.282i	−0.266191	+	0.642641i	−0.999298	−	0.0374720i	$-0.988070\pi$
$349$	−92.9006	+	224.282i	−0.266191	+	0.642641i	0.733107	+	0.680113i	$0.238070\pi$
$350$		0			0
$351$			12.7046i			0.0361955i
$352$		0			0
$353$	453.234			1.28395			0.641975	−	0.766726i	$-0.278115\pi$
$353$	453.234			1.28395			0.641975	+	0.766726i	$0.278115\pi$
$354$		0			0
$355$	−105.357	−	43.6405i	−0.296782	−	0.122931i
$356$		0			0
$357$	233.664	−	96.7866i	0.654520	−	0.271111i
$358$		0			0
$359$	−175.857	−	175.857i	−0.489852	−	0.489852i	0.418407	−	0.908259i	$-0.362588\pi$
$359$	−175.857	−	175.857i	−0.489852	−	0.489852i	−0.908259	+	0.418407i	$0.862588\pi$
$360$		0			0
$361$	1.44333	+	1.44333i	0.00399816	+	0.00399816i
$362$		0			0
$363$	−184.161	+	76.2821i	−0.507332	+	0.210144i
$364$		0			0
$365$	76.0082	+	31.4836i	0.208242	+	0.0862566i
$366$		0			0
$367$	−115.194			−0.313879			−0.156939	−	0.987608i	$-0.550163\pi$
$367$	−115.194			−0.313879			−0.156939	+	0.987608i	$0.550163\pi$
$368$		0			0
$369$		−	334.398i		−	0.906228i
$370$		0			0
$371$	63.9394	−	154.363i	0.172343	−	0.416074i
$372$		0			0
$373$	−95.1961	−	229.824i	−0.255217	−	0.616149i	0.743393	−	0.668855i	$-0.233215\pi$
$373$	−95.1961	−	229.824i	−0.255217	−	0.616149i	−0.998610	+	0.0527059i	$0.983215\pi$
$374$		0			0
$375$	161.629	−	161.629i	0.431011	−	0.431011i
$376$		0			0
$377$	−16.3692	+	16.3692i	−0.0434197	+	0.0434197i
$378$		0			0
$379$	−264.738	−	639.134i	−0.698517	−	1.68637i	−0.726873	−	0.686772i	$-0.759027\pi$
$379$	−264.738	−	639.134i	−0.698517	−	1.68637i	0.0283560	−	0.999598i	$-0.490973\pi$
$380$		0			0
$381$	−38.9277	+	93.9798i	−0.102172	+	0.246666i
$382$		0			0
$383$			217.725i			0.568473i	0.958754	+	0.284236i	$0.0917401\pi$
$383$			217.725i			0.568473i	−0.958754	+	0.284236i	$0.908260\pi$
$384$		0			0
$385$	−388.455			−1.00897
$386$		0			0
$387$	−86.7145	−	35.9183i	−0.224068	−	0.0928122i
$388$		0			0
$389$	452.405	−	187.392i	1.16299	−	0.481728i	0.284123	−	0.958788i	$-0.408297\pi$
$389$	452.405	−	187.392i	1.16299	−	0.481728i	0.878871	+	0.477060i	$0.158297\pi$
$390$		0			0
$391$	20.6092	+	20.6092i	0.0527091	+	0.0527091i
$392$		0			0
$393$	−231.205	−	231.205i	−0.588308	−	0.588308i
$394$		0			0
$395$	603.823	−	250.112i	1.52866	−	0.633194i
$396$		0			0
$397$	−281.846	−	116.745i	−0.709940	−	0.294067i	−0.00166042	−	0.999999i	$-0.500529\pi$
$397$	−281.846	−	116.745i	−0.709940	−	0.294067i	−0.708280	+	0.705932i	$0.750529\pi$
$398$		0			0
$399$	180.390			0.452105
$400$		0			0
$401$		−	173.814i		−	0.433452i	−0.976232	−	0.216726i	$-0.930462\pi$
$401$		−	173.814i		−	0.433452i	0.976232	−	0.216726i	$-0.0695378\pi$
$402$		0			0
$403$	−7.47829	+	18.0542i	−0.0185565	+	0.0447995i
$404$		0			0
$405$	18.1090	+	43.7190i	0.0447136	+	0.107948i
$406$		0			0
$407$	430.110	−	430.110i	1.05678	−	1.05678i
$408$		0			0
$409$	322.065	−	322.065i	0.787446	−	0.787446i	−0.193629	−	0.981075i	$-0.562026\pi$
$409$	322.065	−	322.065i	0.787446	−	0.787446i	0.981075	+	0.193629i	$0.0620258\pi$
$410$		0			0
$411$	128.537	+	310.315i	0.312742	+	0.755025i
$412$		0			0
$413$	29.5039	−	71.2287i	0.0714380	−	0.172467i
$414$		0			0
$415$		−	130.198i		−	0.313730i
$416$		0			0
$417$	−118.179			−0.283403
$418$		0			0
$419$	−13.9903	−	5.79496i	−0.0333896	−	0.0138304i	0.365926	−	0.930644i	$-0.380752\pi$
$419$	−13.9903	−	5.79496i	−0.0333896	−	0.0138304i	−0.399316	+	0.916813i	$0.630752\pi$
$420$		0			0
$421$	−507.883	+	210.372i	−1.20637	+	0.499696i	−0.893053	−	0.449952i	$-0.851441\pi$
$421$	−507.883	+	210.372i	−1.20637	+	0.499696i	−0.313320	+	0.949648i	$0.601441\pi$
$422$		0			0
$423$	266.790	+	266.790i	0.630708	+	0.630708i
$424$		0			0
$425$	83.4900	+	83.4900i	0.196447	+	0.196447i
$426$		0			0
$427$	−189.833	+	78.6313i	−0.444573	+	0.184148i
$428$		0			0
$429$	−12.0025	−	4.97159i	−0.0279778	−	0.0115888i
$430$		0			0
$431$	−654.734			−1.51910			−0.759552	−	0.650447i	$-0.774582\pi$
$431$	−654.734			−1.51910			−0.759552	+	0.650447i	$0.774582\pi$
$432$		0			0
$433$		−	366.488i		−	0.846392i	−0.906038	−	0.423196i	$-0.860908\pi$
$433$		−	366.488i		−	0.846392i	0.906038	−	0.423196i	$-0.139092\pi$
$434$		0			0
$435$	139.660	−	337.170i	0.321058	−	0.775103i
$436$		0			0
$437$	7.95524	+	19.2057i	0.0182042	+	0.0439489i
$438$		0			0
$439$	−124.489	+	124.489i	−0.283573	+	0.283573i	−0.834532	−	0.550959i	$-0.814262\pi$
$439$	−124.489	+	124.489i	−0.283573	+	0.283573i	0.550959	+	0.834532i	$0.314262\pi$
$440$		0			0
$441$	−77.5759	+	77.5759i	−0.175909	+	0.175909i
$442$		0			0
$443$	−147.480	−	356.047i	−0.332911	−	0.803718i	−0.998359	−	0.0572735i	$-0.981759\pi$
$443$	−147.480	−	356.047i	−0.332911	−	0.803718i	0.665448	−	0.746445i	$-0.268241\pi$
$444$		0			0
$445$	−14.5322	+	35.0839i	−0.0326567	+	0.0788402i
$446$		0			0
$447$		−	185.186i		−	0.414286i
$448$		0			0
$449$	−689.326			−1.53525			−0.767623	−	0.640901i	$-0.778561\pi$
$449$	−689.326			−1.53525			−0.767623	+	0.640901i	$0.778561\pi$
$450$		0			0
$451$	784.465	+	324.936i	1.73939	+	0.720479i
$452$		0			0
$453$	355.788	−	147.372i	0.785403	−	0.325325i
$454$		0			0
$455$	−8.77817	−	8.77817i	−0.0192927	−	0.0192927i
$456$		0			0
$457$	86.4503	+	86.4503i	0.189169	+	0.189169i	0.795337	−	0.606168i	$-0.207294\pi$
$457$	86.4503	+	86.4503i	0.189169	+	0.189169i	−0.606168	+	0.795337i	$0.707294\pi$
$458$		0			0
$459$	633.181	−	262.272i	1.37948	−	0.571399i
$460$		0			0
$461$	−3.31579	−	1.37344i	−0.00719259	−	0.00297927i	0.379084	−	0.925362i	$-0.376239\pi$
$461$	−3.31579	−	1.37344i	−0.00719259	−	0.00297927i	−0.386277	+	0.922383i	$0.626239\pi$
$462$		0			0
$463$	−113.007			−0.244075			−0.122038	−	0.992525i	$-0.538943\pi$
$463$	−113.007			−0.244075			−0.122038	+	0.992525i	$0.538943\pi$
$464$		0			0
$465$		−	308.072i		−	0.662521i
$466$		0			0
$467$	150.402	−	363.102i	0.322059	−	0.777520i	−0.677075	−	0.735914i	$-0.736753\pi$
$467$	150.402	−	363.102i	0.322059	−	0.777520i	0.999134	−	0.0416055i	$-0.0132473\pi$
$468$		0			0
$469$	60.1753	+	145.276i	0.128306	+	0.309757i
$470$		0			0
$471$	−99.9053	+	99.9053i	−0.212113	+	0.212113i
$472$		0			0
$473$	168.522	−	168.522i	0.356282	−	0.356282i
$474$		0			0
$475$	32.2275	+	77.8040i	0.0678473	+	0.163798i
$476$		0			0
$477$	69.7759	−	168.454i	0.146281	−	0.353153i
$478$		0			0
$479$			205.624i			0.429278i	0.976693	+	0.214639i	$0.0688575\pi$
$479$			205.624i			0.429278i	−0.976693	+	0.214639i	$0.931142\pi$
$480$		0			0
$481$	19.4390			0.0404136
$482$		0			0
$483$	−9.65155	−	3.99780i	−0.0199825	−	0.00827702i
$484$		0			0
$485$	280.302	−	116.105i	0.577942	−	0.239391i
$486$		0			0
$487$	−573.249	−	573.249i	−1.17710	−	1.17710i	−0.980479	−	0.196623i	$-0.937002\pi$
$487$	−573.249	−	573.249i	−1.17710	−	1.17710i	−0.196623	−	0.980479i	$-0.562998\pi$
$488$		0			0
$489$	−252.477	−	252.477i	−0.516313	−	0.516313i
$490$		0			0
$491$	−421.115	+	174.432i	−0.857669	+	0.355258i	−0.767795	−	0.640695i	$-0.778646\pi$
$491$	−421.115	+	174.432i	−0.857669	+	0.355258i	−0.0898735	+	0.995953i	$0.528646\pi$
$492$		0			0
$493$	1153.74	+	477.897i	2.34025	+	0.969364i
$494$		0			0
$495$	−423.914			−0.856392
$496$		0			0
$497$			139.867i			0.281423i
$498$		0			0
$499$	−115.301	+	278.361i	−0.231064	+	0.557837i	−0.996303	−	0.0859086i	$-0.972621\pi$
$499$	−115.301	+	278.361i	−0.231064	+	0.557837i	0.765239	+	0.643746i	$0.222621\pi$
$500$		0			0
$501$	71.1147	+	171.686i	0.141946	+	0.342687i
$502$		0			0
$503$	−526.474	+	526.474i	−1.04667	+	1.04667i	−0.0478110	+	0.998856i	$0.515225\pi$
$503$	−526.474	+	526.474i	−1.04667	+	1.04667i	−0.998856	+	0.0478110i	$0.984775\pi$
$504$		0			0
$505$	81.0930	−	81.0930i	0.160580	−	0.160580i
$506$		0			0
$507$	110.578	+	266.958i	0.218102	+	0.526545i
$508$		0			0
$509$	−98.1719	+	237.008i	−0.192872	+	0.465634i	−0.990500	−	0.137516i	$-0.956088\pi$
$509$	−98.1719	+	237.008i	−0.192872	+	0.465634i	0.797628	+	0.603150i	$0.206088\pi$
$510$		0			0
$511$		−	100.905i		−	0.197465i
$512$		0			0
$513$	488.821			0.952867
$514$		0			0
$515$	92.0858	+	38.1432i	0.178807	+	0.0740644i
$516$		0			0
$517$	−885.103	+	366.622i	−1.71200	+	0.709133i
$518$		0			0
$519$	−60.2895	−	60.2895i	−0.116165	−	0.116165i
$520$		0			0
$521$	−42.3980	−	42.3980i	−0.0813781	−	0.0813781i	0.665246	−	0.746624i	$-0.268327\pi$
$521$	−42.3980	−	42.3980i	−0.0813781	−	0.0813781i	−0.746624	+	0.665246i	$0.768327\pi$
$522$		0			0
$523$	−160.929	+	66.6589i	−0.307703	+	0.127455i	−0.531192	−	0.847252i	$-0.678256\pi$
$523$	−160.929	+	66.6589i	−0.307703	+	0.127455i	0.223488	+	0.974707i	$0.428256\pi$
$524$		0			0
$525$	−39.0993	−	16.1955i	−0.0744749	−	0.0308485i
$526$		0			0
$527$	1054.18			2.00034
$528$		0			0
$529$			527.796i			0.997724i
$530$		0			0
$531$	32.1971	−	77.7306i	0.0606348	−	0.146385i
$532$		0			0
$533$	10.3843	+	25.0698i	0.0194827	+	0.0470353i
$534$		0			0
$535$	−371.497	+	371.497i	−0.694386	+	0.694386i
$536$		0			0
$537$	−93.2687	+	93.2687i	−0.173685	+	0.173685i
$538$		0			0
$539$	−106.605	−	257.366i	−0.197782	−	0.477488i
$540$		0			0
$541$	−29.6178	+	71.5038i	−0.0547465	+	0.132170i	−0.948886	−	0.315618i	$-0.897788\pi$
$541$	−29.6178	+	71.5038i	−0.0547465	+	0.132170i	0.894140	+	0.447788i	$0.147788\pi$
$542$		0			0
$543$		−	209.121i		−	0.385121i
$544$		0			0
$545$	403.937			0.741169
$546$		0			0
$547$	−157.659	−	65.3046i	−0.288225	−	0.119387i	0.233886	−	0.972264i	$-0.424856\pi$
$547$	−157.659	−	65.3046i	−0.288225	−	0.119387i	−0.522112	+	0.852877i	$0.674856\pi$
$548$		0			0
$549$	−207.161	+	85.8089i	−0.377342	+	0.156300i
$550$		0			0
$551$	629.819	+	629.819i	1.14305	+	1.14305i
$552$		0			0
$553$	−566.819	−	566.819i	−1.02499	−	1.02499i
$554$		0			0
$555$	−283.125	+	117.274i	−0.510136	+	0.211305i
$556$		0			0
$557$	−890.709	−	368.944i	−1.59912	−	0.662376i	−0.607827	−	0.794069i	$-0.707959\pi$
$557$	−890.709	−	368.944i	−1.59912	−	0.662376i	−0.991291	+	0.131693i	$0.957959\pi$
$558$		0			0
$559$	7.61638			0.0136250
$560$		0			0
$561$			700.821i			1.24923i
$562$		0			0
$563$	−106.191	+	256.369i	−0.188617	+	0.455362i	−0.989694	−	0.143200i	$-0.954261\pi$
$563$	−106.191	+	256.369i	−0.188617	+	0.455362i	0.801077	+	0.598562i	$0.204261\pi$
$564$		0			0
$565$	17.2037	+	41.5333i	0.0304490	+	0.0735103i
$566$		0			0
$567$	41.0398	−	41.0398i	0.0723806	−	0.0723806i
$568$		0			0
$569$	−351.714	+	351.714i	−0.618126	+	0.618126i	−0.945050	−	0.326925i	$-0.893988\pi$
$569$	−351.714	+	351.714i	−0.618126	+	0.618126i	0.326925	+	0.945050i	$0.393988\pi$
$570$		0			0
$571$	−179.708	−	433.854i	−0.314725	−	0.759814i	−0.999517	−	0.0310755i	$-0.990107\pi$
$571$	−179.708	−	433.854i	−0.314725	−	0.759814i	0.684792	−	0.728739i	$-0.259893\pi$
$572$		0			0
$573$	148.987	−	359.688i	0.260013	−	0.627727i
$574$		0			0
$575$		−	4.87703i		−	0.00848179i
$576$		0			0
$577$	662.602			1.14836			0.574179	−	0.818730i	$-0.305321\pi$
$577$	662.602			1.14836			0.574179	+	0.818730i	$0.305321\pi$
$578$		0			0
$579$	73.4898	+	30.4405i	0.126925	+	0.0525742i
$580$		0			0
$581$	−147.532	+	61.1096i	−0.253927	+	0.105180i
$582$		0			0
$583$	327.375	+	327.375i	0.561535	+	0.561535i
$584$		0			0
$585$	−9.57946	−	9.57946i	−0.0163751	−	0.0163751i
$586$		0			0
$587$	−650.448	+	269.424i	−1.10809	+	0.458985i	−0.860279	−	0.509824i	$-0.829711\pi$
$587$	−650.448	+	269.424i	−1.10809	+	0.458985i	−0.247809	+	0.968809i	$0.579711\pi$
$588$		0			0
$589$	694.650	+	287.733i	1.17937	+	0.488512i
$590$		0			0
$591$	345.625			0.584814
$592$		0			0
$593$			430.692i			0.726293i	0.931732	+	0.363147i	$0.118298\pi$
$593$			430.692i			0.726293i	−0.931732	+	0.363147i	$0.881702\pi$
$594$		0			0
$595$	−256.277	+	618.708i	−0.430718	+	1.03985i
$596$		0			0
$597$	50.5082	+	121.938i	0.0846033	+	0.204250i
$598$		0			0
$599$	16.0528	−	16.0528i	0.0267993	−	0.0267993i	−0.693580	−	0.720379i	$-0.743968\pi$
$599$	16.0528	−	16.0528i	0.0267993	−	0.0267993i	0.720379	+	0.693580i	$0.243968\pi$
$600$		0			0
$601$	201.233	−	201.233i	0.334831	−	0.334831i	−0.519587	−	0.854418i	$-0.673914\pi$
$601$	201.233	−	201.233i	0.334831	−	0.334831i	0.854418	+	0.519587i	$0.173914\pi$
$602$		0			0
$603$	65.6682	+	158.537i	0.108902	+	0.262914i
$604$		0			0
$605$	201.984	−	487.633i	0.333858	−	0.806005i
$606$		0			0
$607$		−	713.329i		−	1.17517i	−0.809162	−	0.587586i	$-0.800079\pi$
$607$		−	713.329i		−	1.17517i	0.809162	−	0.587586i	$-0.199921\pi$
$608$		0			0
$609$	−447.609			−0.734990
$610$		0			0
$611$	−28.2860	−	11.7164i	−0.0462946	−	0.0191759i
$612$		0			0
$613$	−349.658	+	144.833i	−0.570404	+	0.236269i	−0.649195	−	0.760622i	$-0.724894\pi$
$613$	−349.658	+	144.833i	−0.570404	+	0.236269i	0.0787907	+	0.996891i	$0.474894\pi$
$614$		0			0
$615$	−302.490	−	302.490i	−0.491854	−	0.491854i
$616$		0			0
$617$	185.331	+	185.331i	0.300374	+	0.300374i	0.841160	−	0.540786i	$-0.181873\pi$
$617$	185.331	+	185.331i	0.300374	+	0.300374i	−0.540786	+	0.841160i	$0.681873\pi$
$618$		0			0
$619$	740.280	−	306.634i	1.19593	−	0.495370i	0.306248	−	0.951952i	$-0.400926\pi$
$619$	740.280	−	306.634i	1.19593	−	0.495370i	0.889681	+	0.456582i	$0.150926\pi$
$620$		0			0
$621$	−26.1538	−	10.8332i	−0.0421156	−	0.0174448i
$622$		0			0
$623$	46.5755			0.0747601
$624$		0			0
$625$			494.120i			0.790591i
$626$		0			0
$627$	−191.286	+	461.805i	−0.305081	+	0.736532i
$628$		0			0
$629$	−401.295	−	968.812i	−0.637989	−	1.54024i
$630$		0			0
$631$	−25.0415	+	25.0415i	−0.0396854	+	0.0396854i	−0.726671	−	0.686986i	$-0.758934\pi$
$631$	−25.0415	+	25.0415i	−0.0396854	+	0.0396854i	0.686986	+	0.726671i	$0.258934\pi$
$632$		0			0
$633$	110.919	−	110.919i	0.175227	−	0.175227i
$634$		0			0
$635$	−103.075	−	248.845i	−0.162323	−	0.391882i
$636$		0			0
$637$	3.40686	−	8.22488i	0.00534828	−	0.0129119i
$638$		0			0
$639$			152.634i			0.238864i
$640$		0			0
$641$	−150.813			−0.235278			−0.117639	−	0.993056i	$-0.537533\pi$
$641$	−150.813			−0.235278			−0.117639	+	0.993056i	$0.537533\pi$
$642$		0			0
$643$	635.355	+	263.173i	0.988110	+	0.409289i	0.817424	−	0.576037i	$-0.195402\pi$
$643$	635.355	+	263.173i	0.988110	+	0.409289i	0.170686	+	0.985325i	$0.445402\pi$
$644$		0			0
$645$	−110.931	+	45.9492i	−0.171987	+	0.0712391i
$646$		0			0
$647$	460.454	+	460.454i	0.711675	+	0.711675i	0.966885	−	0.255211i	$-0.0821448\pi$
$647$	460.454	+	460.454i	0.711675	+	0.711675i	−0.255211	+	0.966885i	$0.582145\pi$
$648$		0			0
$649$	151.062	+	151.062i	0.232762	+	0.232762i
$650$		0			0
$651$	−349.087	+	144.597i	−0.536232	+	0.222115i
$652$		0			0
$653$	308.661	+	127.852i	0.472682	+	0.195791i	0.606291	−	0.795243i	$-0.292657\pi$
$653$	308.661	+	127.852i	0.472682	+	0.195791i	−0.133609	+	0.991034i	$0.542657\pi$
$654$		0			0
$655$	865.779			1.32180
$656$		0			0
$657$		−	110.115i		−	0.167603i
$658$		0			0
$659$	187.311	−	452.209i	0.284235	−	0.686205i	−0.715690	−	0.698418i	$-0.753888\pi$
$659$	187.311	−	452.209i	0.284235	−	0.686205i	0.999925	+	0.0122131i	$0.00388764\pi$
$660$		0			0
$661$	−279.659	−	675.156i	−0.423084	−	1.02142i	−0.981432	−	0.191809i	$-0.938564\pi$
$661$	−279.659	−	675.156i	−0.423084	−	1.02142i	0.558348	−	0.829607i	$-0.311436\pi$
$662$		0			0
$663$	−15.8369	+	15.8369i	−0.0238867	+	0.0238867i
$664$		0			0
$665$	−337.747	+	337.747i	−0.507891	+	0.507891i
$666$		0			0
$667$	−19.7397	−	47.6558i	−0.0295947	−	0.0714479i
$668$		0			0
$669$	−280.535	+	677.271i	−0.419335	+	1.01236i
$670$		0			0
$671$		−	569.360i		−	0.848525i
$672$		0			0
$673$	74.6107			0.110863			0.0554314	−	0.998462i	$-0.482347\pi$
$673$	74.6107			0.110863			0.0554314	+	0.998462i	$0.482347\pi$
$674$		0			0
$675$	−105.951	−	43.8865i	−0.156965	−	0.0650170i
$676$		0			0
$677$	−250.770	+	103.872i	−0.370413	+	0.153430i	−0.560122	−	0.828410i	$-0.689246\pi$
$677$	−250.770	+	103.872i	−0.370413	+	0.153430i	0.189709	+	0.981840i	$0.439246\pi$
$678$		0			0
$679$	−263.124	−	263.124i	−0.387517	−	0.387517i
$680$		0			0
$681$	−147.031	−	147.031i	−0.215905	−	0.215905i
$682$		0			0
$683$	−1198.32	+	496.359i	−1.75449	+	0.726734i	−0.757200	+	0.653183i	$0.773433\pi$
$683$	−1198.32	+	496.359i	−1.75449	+	0.726734i	−0.997291	+	0.0735510i	$0.976567\pi$
$684$		0			0
$685$	−821.671	−	340.347i	−1.19952	−	0.496857i
$686$		0			0
$687$	−237.286			−0.345395
$688$		0			0
$689$			14.7958i			0.0214743i
$690$		0			0
$691$	337.819	−	815.567i	0.488884	−	1.18027i	−0.466398	−	0.884575i	$-0.654449\pi$
$691$	337.819	−	815.567i	0.488884	−	1.18027i	0.955282	−	0.295696i	$-0.0955514\pi$
$692$		0			0
$693$	198.968	+	480.351i	0.287111	+	0.693147i
$694$		0			0
$695$	221.269	−	221.269i	0.318372	−	0.318372i
$696$		0			0
$697$	1035.08	−	1035.08i	1.48504	−	1.48504i
$698$		0			0
$699$	83.9591	+	202.695i	0.120113	+	0.289979i
$700$		0			0
$701$	487.432	−	1176.77i	0.695338	−	1.67870i	−0.0383989	−	0.999262i	$-0.512226\pi$
$701$	487.432	−	1176.77i	0.695338	−	1.67870i	0.733737	−	0.679433i	$-0.237774\pi$
$702$		0			0
$703$		−	747.930i		−	1.06391i
$704$		0			0
$705$	482.666			0.684632
$706$		0			0
$707$	−129.951	−	53.8274i	−0.183806	−	0.0761349i
$708$		0			0
$709$	949.384	−	393.248i	1.33905	−	0.554651i	0.405824	−	0.913951i	$-0.366985\pi$
$709$	949.384	−	393.248i	1.33905	−	0.554651i	0.933222	+	0.359300i	$0.116985\pi$
$710$		0			0
$711$	−618.559	−	618.559i	−0.869985	−	0.869985i
$712$		0			0
$713$	−30.7896	−	30.7896i	−0.0431832	−	0.0431832i
$714$		0			0
$715$	31.7809	−	13.1641i	0.0444487	−	0.0184113i
$716$		0			0
$717$	448.906	+	185.943i	0.626089	+	0.259335i
$718$		0			0
$719$	−349.072			−0.485496			−0.242748	−	0.970089i	$-0.578049\pi$
$719$	−349.072			−0.485496			−0.242748	+	0.970089i	$0.578049\pi$
$720$		0			0
$721$		−	122.248i		−	0.169554i
$722$		0			0
$723$	202.788	−	489.573i	0.280481	−	0.677141i
$724$		0			0
$725$	−79.9673	−	193.058i	−0.110300	−	0.266287i
$726$		0			0
$727$	256.931	−	256.931i	0.353413	−	0.353413i	−0.507965	−	0.861378i	$-0.669602\pi$
$727$	256.931	−	256.931i	0.353413	−	0.353413i	0.861378	+	0.507965i	$0.169602\pi$
$728$		0			0
$729$	−236.352	+	236.352i	−0.324214	+	0.324214i
$730$		0			0
$731$	−157.231	−	379.590i	−0.215091	−	0.519275i
$732$		0			0
$733$	473.293	−	1142.63i	0.645694	−	1.55884i	−0.173194	−	0.984888i	$-0.555409\pi$
$733$	473.293	−	1142.63i	0.645694	−	1.55884i	0.818887	−	0.573955i	$-0.194591\pi$
$734$		0			0
$735$			140.347i			0.190949i
$736$		0			0
$737$	−435.722			−0.591211
$738$		0			0
$739$	137.009	+	56.7511i	0.185398	+	0.0767945i	0.473451	−	0.880820i	$-0.343008\pi$
$739$	137.009	+	56.7511i	0.185398	+	0.0767945i	−0.288053	+	0.957614i	$0.593008\pi$
$740$		0			0
$741$	−14.7583	+	6.11310i	−0.0199168	+	0.00824979i
$742$		0			0
$743$	644.593	+	644.593i	0.867555	+	0.867555i	0.992201	−	0.124647i	$-0.0397797\pi$
$743$	644.593	+	644.593i	0.867555	+	0.867555i	−0.124647	+	0.992201i	$0.539780\pi$
$744$		0			0
$745$	346.727	+	346.727i	0.465405	+	0.465405i
$746$		0			0
$747$	−160.999	+	66.6878i	−0.215527	+	0.0892742i
$748$		0			0
$749$	595.321	+	246.590i	0.794821	+	0.329225i
$750$		0			0
$751$	18.5402			0.0246873			0.0123437	−	0.999924i	$-0.496071\pi$
$751$	18.5402			0.0246873			0.0123437	+	0.999924i	$0.496071\pi$
$752$		0			0
$753$		−	151.836i		−	0.201641i
$754$		0			0
$755$	−390.220	+	942.075i	−0.516848	+	1.24778i
$756$		0			0
$757$	100.854	+	243.482i	0.133228	+	0.321641i	0.976389	−	0.216021i	$-0.0693079\pi$
$757$	100.854	+	243.482i	0.133228	+	0.321641i	−0.843161	+	0.537661i	$0.819308\pi$
$758$		0			0
$759$	20.4691	−	20.4691i	0.0269685	−	0.0269685i
$760$		0			0
$761$	−272.267	+	272.267i	−0.357775	+	0.357775i	−0.862992	−	0.505217i	$-0.831412\pi$
$761$	−272.267	+	272.267i	−0.357775	+	0.357775i	0.505217	+	0.862992i	$0.331412\pi$
$762$		0			0
$763$	−189.591	−	457.714i	−0.248482	−	0.599888i
$764$		0			0
$765$	−279.671	+	675.185i	−0.365583	+	0.882594i
$766$		0			0
$767$			6.82730i			0.00890130i
$768$		0			0
$769$	−341.927			−0.444638			−0.222319	−	0.974974i	$-0.571363\pi$
$769$	−341.927			−0.444638			−0.222319	+	0.974974i	$0.571363\pi$
$770$		0			0
$771$	−305.417	−	126.508i	−0.396131	−	0.164083i
$772$		0			0
$773$	−366.728	+	151.904i	−0.474421	+	0.196512i	−0.607065	−	0.794652i	$-0.707653\pi$
$773$	−366.728	+	151.904i	−0.474421	+	0.196512i	0.132644	+	0.991164i	$0.457653\pi$
$774$		0			0
$775$	−124.732	−	124.732i	−0.160944	−	0.160944i
$776$		0			0
$777$	265.775	+	265.775i	0.342053	+	0.342053i
$778$		0			0
$779$	964.582	−	399.543i	1.23823	−	0.512892i
$780$		0			0
$781$	−358.065	−	148.315i	−0.458470	−	0.189904i
$782$		0			0
$783$	−1212.93			−1.54908
$784$		0			0
$785$		−	374.109i		−	0.476572i
$786$		0			0
$787$	−167.684	+	404.824i	−0.213067	+	0.514389i	−0.993892	−	0.110361i	$-0.964799\pi$
$787$	−167.684	+	404.824i	−0.213067	+	0.514389i	0.780825	+	0.624750i	$0.214799\pi$
$788$		0			0
$789$	−13.4179	−	32.3938i	−0.0170063	−	0.0410568i
$790$		0			0
$791$	38.9881	−	38.9881i	0.0492896	−	0.0492896i
$792$		0			0
$793$	12.8662	−	12.8662i	0.0162247	−	0.0162247i
$794$		0			0
$795$	−89.2623	−	215.498i	−0.112280	−	0.271067i
$796$		0			0
$797$	−230.548	+	556.591i	−0.289269	+	0.698358i	−0.999987	−	0.00511971i	$-0.998370\pi$
$797$	−230.548	+	556.591i	−0.289269	+	0.698358i	0.710718	+	0.703477i	$0.248370\pi$
$798$		0			0
$799$			1651.61i			2.06710i
$800$		0			0
$801$	50.8270			0.0634545
$802$		0			0
$803$	258.320	+	106.999i	0.321693	+	0.133250i
$804$		0			0
$805$	25.5559	−	10.5856i	0.0317465	−	0.0131498i
$806$		0			0
$807$	165.058	+	165.058i	0.204533	+	0.204533i
$808$		0			0
$809$	195.031	+	195.031i	0.241077	+	0.241077i	0.817296	−	0.576219i	$-0.195472\pi$
$809$	195.031	+	195.031i	0.241077	+	0.241077i	−0.576219	+	0.817296i	$0.695472\pi$
$810$		0			0
$811$	889.956	−	368.632i	1.09736	−	0.454540i	0.240791	−	0.970577i	$-0.422593\pi$
$811$	889.956	−	368.632i	1.09736	−	0.454540i	0.856566	+	0.516037i	$0.172593\pi$
$812$		0			0
$813$	−776.161	−	321.496i	−0.954688	−	0.395445i
$814$		0			0
$815$	945.435			1.16004
$816$		0			0
$817$		−	293.046i		−	0.358686i
$818$		0			0
$819$	−6.35859	+	15.3510i	−0.00776385	+	0.0187436i
$820$		0			0
$821$	328.443	+	792.932i	0.400052	+	0.965812i	0.987653	+	0.156660i	$0.0500728\pi$
$821$	328.443	+	792.932i	0.400052	+	0.965812i	−0.587600	+	0.809151i	$0.699927\pi$
$822$		0			0
$823$	319.915	−	319.915i	0.388718	−	0.388718i	−0.485512	−	0.874230i	$-0.661367\pi$
$823$	319.915	−	319.915i	0.388718	−	0.388718i	0.874230	+	0.485512i	$0.161367\pi$
$824$		0			0
$825$	82.9221	−	82.9221i	0.100512	−	0.100512i
$826$		0			0
$827$	352.335	+	850.612i	0.426040	+	1.02855i	0.980532	+	0.196362i	$0.0629127\pi$
$827$	352.335	+	850.612i	0.426040	+	1.02855i	−0.554492	+	0.832189i	$0.687087\pi$
$828$		0			0
$829$	−459.660	+	1109.72i	−0.554475	+	1.33862i	0.359611	+	0.933102i	$0.382909\pi$
$829$	−459.660	+	1109.72i	−0.554475	+	1.33862i	−0.914086	+	0.405519i	$0.867091\pi$
$830$		0			0
$831$			821.783i			0.988908i
$832$		0			0
$833$	−480.248			−0.576528
$834$		0			0
$835$	−454.600	−	188.302i	−0.544432	−	0.225511i
$836$		0			0
$837$	−945.956	+	391.828i	−1.13017	+	0.468133i
$838$		0			0
$839$	−439.790	−	439.790i	−0.524184	−	0.524184i	0.394648	−	0.918832i	$-0.370866\pi$
$839$	−439.790	−	439.790i	−0.524184	−	0.524184i	−0.918832	+	0.394648i	$0.870866\pi$
$840$		0			0
$841$	−968.120	−	968.120i	−1.15115	−	1.15115i
$842$		0			0
$843$	367.953	−	152.411i	0.436480	−	0.180796i
$844$		0			0
$845$	−706.868	−	292.794i	−0.836530	−	0.346502i
$846$		0			0
$847$	−647.356			−0.764293
$848$		0			0
$849$		−	441.361i		−	0.519860i
$850$		0			0
$851$	−16.5756	+	40.0171i	−0.0194778	+	0.0470236i
$852$		0			0
$853$	639.942	+	1544.96i	0.750225	+	1.81120i	0.557977	+	0.829857i	$0.311578\pi$
$853$	639.942	+	1544.96i	0.750225	+	1.81120i	0.192248	+	0.981346i	$0.438422\pi$
$854$		0			0
$855$	−368.578	+	368.578i	−0.431085	+	0.431085i
$856$		0			0
$857$	−628.373	+	628.373i	−0.733224	+	0.733224i	−0.971257	−	0.238033i	$-0.923497\pi$
$857$	−628.373	+	628.373i	−0.733224	+	0.733224i	0.238033	+	0.971257i	$0.423497\pi$
$858$		0			0
$859$	467.557	+	1128.78i	0.544304	+	1.31407i	0.921660	+	0.387998i	$0.126833\pi$
$859$	467.557	+	1128.78i	0.544304	+	1.31407i	−0.377357	+	0.926068i	$0.623167\pi$
$860$		0			0
$861$	−200.785	+	484.738i	−0.233200	+	0.562994i
$862$		0			0
$863$			709.297i			0.821896i	0.911659	+	0.410948i	$0.134802\pi$
$863$			709.297i			0.821896i	−0.911659	+	0.410948i	$0.865198\pi$
$864$		0			0
$865$	225.762			0.260997
$866$		0			0
$867$	659.054	+	272.989i	0.760155	+	0.314866i
$868$		0			0
$869$	2052.14	−	850.023i	2.36149	−	0.978162i
$870$		0			0
$871$	−9.84629	−	9.84629i	−0.0113046	−	0.0113046i
$872$		0			0
$873$	−287.143	−	287.143i	−0.328915	−	0.328915i
$874$		0			0
$875$	685.820	−	284.076i	0.783795	−	0.324658i
$876$		0			0
$877$	927.972	+	384.378i	1.05812	+	0.438288i	0.842784	−	0.538252i	$-0.180915\pi$
$877$	927.972	+	384.378i	1.05812	+	0.438288i	0.215337	+	0.976540i	$0.430915\pi$
$878$		0			0
$879$	112.225			0.127673
$880$		0			0
$881$		−	660.780i		−	0.750034i	−0.927018	−	0.375017i	$-0.877637\pi$
$881$		−	660.780i		−	0.750034i	0.927018	−	0.375017i	$-0.122363\pi$
$882$		0			0
$883$	476.753	−	1150.98i	0.539924	−	1.30349i	−0.384851	−	0.922979i	$-0.625747\pi$
$883$	476.753	−	1150.98i	0.539924	−	1.30349i	0.924775	−	0.380514i	$-0.124253\pi$
$884$		0			0
$885$	−41.1888	−	99.4385i	−0.0465410	−	0.112360i
$886$		0			0
$887$	−248.725	+	248.725i	−0.280411	+	0.280411i	−0.833273	−	0.552862i	$-0.813536\pi$
$887$	−248.725	+	248.725i	−0.280411	+	0.280411i	0.552862	+	0.833273i	$0.313536\pi$
$888$		0			0
$889$	−233.595	+	233.595i	−0.262762	+	0.262762i
$890$		0			0
$891$	61.5448	+	148.582i	0.0690738	+	0.166759i
$892$		0			0
$893$	−450.800	+	1088.33i	−0.504815	+	1.21873i
$894$		0			0
$895$		−	349.257i		−	0.390232i
$896$		0			0
$897$	0.925104			0.00103133
$898$		0			0
$899$	−1723.66	−	713.964i	−1.91731	−	0.794176i
$900$		0			0
$901$	737.403	−	305.442i	0.818427	−	0.339004i
$902$		0			0
$903$	104.133	+	104.133i	0.115319	+	0.115319i
$904$		0			0
$905$	391.540	+	391.540i	0.432641	+	0.432641i
$906$		0			0
$907$	−301.032	+	124.692i	−0.331899	+	0.137477i	−0.542409	−	0.840115i	$-0.682488\pi$
$907$	−301.032	+	124.692i	−0.331899	+	0.137477i	0.210510	+	0.977592i	$0.432488\pi$
$908$		0			0
$909$	−141.813	−	58.7409i	−0.156010	−	0.0646214i
$910$		0			0
$911$	−1283.61			−1.40901			−0.704507	−	0.709697i	$-0.748832\pi$
$911$	−1283.61			−1.40901			−0.704507	+	0.709697i	$0.748832\pi$
$912$		0			0
$913$		−	442.488i		−	0.484652i
$914$		0			0
$915$	−109.773	+	265.015i	−0.119970	+	0.289634i
$916$		0			0
$917$	−406.361	−	981.043i	−0.443142	−	1.06984i
$918$		0			0
$919$	−299.609	+	299.609i	−0.326017	+	0.326017i	−0.851070	−	0.525053i	$-0.824046\pi$
$919$	−299.609	+	299.609i	−0.326017	+	0.326017i	0.525053	+	0.851070i	$0.324046\pi$
$920$		0			0
$921$	525.717	−	525.717i	0.570811	−	0.570811i
$922$		0			0
$923$	−4.73985	−	11.4430i	−0.00513526	−	0.0123976i
$924$		0			0
$925$	−67.1494	+	162.113i	−0.0725940	+	0.175257i
$926$		0			0
$927$		−	133.407i		−	0.143913i
$928$		0			0
$929$	166.333			0.179045			0.0895225	−	0.995985i	$-0.471466\pi$
$929$	166.333			0.179045			0.0895225	+	0.995985i	$0.471466\pi$
$930$		0			0
$931$	−316.459	−	131.082i	−0.339913	−	0.140797i
$932$		0			0
$933$	−585.329	+	242.451i	−0.627363	+	0.259862i
$934$		0			0
$935$	−1312.16	−	1312.16i	−1.40338	−	1.40338i
$936$		0			0
$937$	919.394	+	919.394i	0.981211	+	0.981211i	0.999827	−	0.0186162i	$-0.00592605\pi$
$937$	919.394	+	919.394i	0.981211	+	0.981211i	−0.0186162	+	0.999827i	$0.505926\pi$
$938$		0			0
$939$	675.000	−	279.594i	0.718850	−	0.297757i
$940$		0			0
$941$	540.855	+	224.029i	0.574766	+	0.238076i	0.651082	−	0.759008i	$-0.274316\pi$
$941$	540.855	+	224.029i	0.574766	+	0.238076i	−0.0763153	+	0.997084i	$0.524316\pi$
$942$		0			0
$943$	−60.4635			−0.0641182
$944$		0			0
$945$		−	650.447i		−	0.688304i
$946$		0			0
$947$	149.824	−	361.708i	0.158209	−	0.381951i	−0.824821	−	0.565394i	$-0.808724\pi$
$947$	149.824	−	361.708i	0.158209	−	0.381951i	0.983030	+	0.183443i	$0.0587241\pi$
$948$		0			0
$949$	3.41948	+	8.25535i	0.00360324	+	0.00869900i
$950$		0			0
$951$	−36.2291	+	36.2291i	−0.0380958	+	0.0380958i
$952$		0			0
$953$	−400.363	+	400.363i	−0.420108	+	0.420108i	−0.885241	−	0.465133i	$-0.846006\pi$
$953$	−400.363	+	400.363i	−0.420108	+	0.420108i	0.465133	+	0.885241i	$0.346006\pi$
$954$		0			0
$955$	394.498	+	952.401i	0.413086	+	0.997279i
$956$		0			0
$957$	474.646	−	1145.90i	0.495973	−	1.19738i
$958$		0			0
$959$			1090.81i			1.13744i
$960$		0			0
$961$	−613.912			−0.638827
$962$		0			0
$963$	649.662	+	269.099i	0.674623	+	0.279438i
$964$		0			0
$965$	−194.590	+	80.6020i	−0.201648	+	0.0835254i
$966$		0			0
$967$	450.402	+	450.402i	0.465772	+	0.465772i	0.900542	−	0.434770i	$-0.143170\pi$
$967$	450.402	+	450.402i	0.465772	+	0.465772i	−0.434770	+	0.900542i	$0.643170\pi$
$968$		0			0
$969$	609.338	+	609.338i	0.628831	+	0.628831i
$970$		0			0
$971$	−1287.15	+	533.155i	−1.32559	+	0.549079i	−0.929395	−	0.369086i	$-0.879671\pi$
$971$	−1287.15	+	533.155i	−1.32559	+	0.549079i	−0.396198	+	0.918165i	$0.629671\pi$
$972$		0			0
$973$	−354.581	−	146.872i	−0.364421	−	0.150948i
$974$		0			0
$975$	3.74769			0.00384378
$976$		0			0
$977$			1408.92i			1.44208i	0.692891	+	0.721042i	$0.256336\pi$
$977$			1408.92i			1.44208i	−0.692891	+	0.721042i	$0.743664\pi$
$978$		0			0
$979$	−49.3888	+	119.235i	−0.0504482	+	0.121793i
$980$		0			0
$981$	−206.898	−	499.495i	−0.210905	−	0.509169i
$982$		0			0
$983$	748.725	−	748.725i	0.761674	−	0.761674i	−0.214951	−	0.976625i	$-0.568959\pi$
$983$	748.725	−	748.725i	0.761674	−	0.761674i	0.976625	+	0.214951i	$0.0689592\pi$
$984$		0			0
$985$	−647.120	+	647.120i	−0.656975	+	0.656975i
$986$		0			0
$987$	−226.544	−	546.925i	−0.229527	−	0.554128i
$988$		0			0
$989$	−6.49449	+	15.6791i	−0.00656673	+	0.0158535i
$990$		0			0
$991$		−	1179.74i		−	1.19045i	−0.803559	−	0.595225i	$-0.797063\pi$
$991$		−	1179.74i		−	1.19045i	0.803559	−	0.595225i	$-0.202937\pi$
$992$		0			0
$993$	−217.455			−0.218988
$994$		0			0
$995$	−322.873	−	133.738i	−0.324496	−	0.134411i
$996$		0			0
$997$	1523.14	−	630.907i	1.52773	−	0.632805i	0.548606	−	0.836081i	$-0.315159\pi$
$997$	1523.14	−	630.907i	1.52773	−	0.632805i	0.979121	+	0.203276i	$0.0651588\pi$
$998$		0			0
$999$	720.196	+	720.196i	0.720917	+	0.720917i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.3.h.a.111.3		28
4.3	odd	2		32.3.h.a.19.1	✓	28
8.3	odd	2		256.3.h.b.223.3		28
8.5	even	2		256.3.h.a.223.5		28
12.11	even	2		288.3.u.a.19.7		28
32.5	even	8		32.3.h.a.27.1	yes	28
32.11	odd	8		256.3.h.a.31.5		28
32.21	even	8		256.3.h.b.31.3		28
32.27	odd	8	inner	128.3.h.a.15.3		28
96.5	odd	8		288.3.u.a.91.7		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.3.h.a.19.1	✓	28	4.3	odd	2
32.3.h.a.27.1	yes	28	32.5	even	8
128.3.h.a.15.3		28	32.27	odd	8	inner
128.3.h.a.111.3		28	1.1	even	1	trivial
256.3.h.a.31.5		28	32.11	odd	8
256.3.h.a.223.5		28	8.5	even	2
256.3.h.b.31.3		28	32.21	even	8
256.3.h.b.223.3		28	8.3	odd	2
288.3.u.a.19.7		28	12.11	even	2
288.3.u.a.91.7		28	96.5	odd	8

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	128.h (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.58190 - 0.655246i) q^{3} +(4.18866 - 1.73500i) q^{5} +(-3.93197 - 3.93197i) q^{7} +(-4.29089 - 4.29089i) q^{9} +O(q^{10})\)	\(q+(-1.58190 - 0.655246i) q^{3} +(4.18866 - 1.73500i) q^{5} +(-3.93197 - 3.93197i) q^{7} +(-4.29089 - 4.29089i) q^{9} +(14.2355 - 5.89652i) q^{11} +(0.454935 + 0.188440i) q^{13} -7.76291 q^{15} -26.5635i q^{17} +(7.25040 - 17.5040i) q^{19} +(3.64359 + 8.79641i) q^{21} +(-0.775848 + 0.775848i) q^{23} +(-3.14303 + 3.14303i) q^{25} +(9.87340 + 23.8365i) q^{27} +(-17.9907 + 43.4334i) q^{29} +39.6852i q^{31} -26.3828 q^{33} +(-23.2916 - 9.64771i) q^{35} +(36.4715 - 15.1070i) q^{37} +(-0.596189 - 0.596189i) q^{39} +(38.9661 + 38.9661i) q^{41} +(14.2899 - 5.91907i) q^{43} +(-25.4177 - 10.5284i) q^{45} -62.1759 q^{47} -18.0792i q^{49} +(-17.4057 + 42.0210i) q^{51} +(11.4986 + 27.7600i) q^{53} +(49.3970 - 49.3970i) q^{55} +(-22.9389 + 22.9389i) q^{57} +(5.30584 + 12.8094i) q^{59} +(14.1407 - 34.1386i) q^{61} +33.7433i q^{63} +2.23251 q^{65} +(-26.1257 - 10.8216i) q^{67} +(1.73569 - 0.718946i) q^{69} +(-17.7859 - 17.7859i) q^{71} +(12.8313 + 12.8313i) q^{73} +(7.03144 - 2.91252i) q^{75} +(-79.1584 - 32.7885i) q^{77} +144.157 q^{79} +10.4375i q^{81} +(10.9897 - 26.5314i) q^{83} +(-46.0877 - 111.266i) q^{85} +(56.9192 - 56.9192i) q^{87} +(-5.92267 + 5.92267i) q^{89} +(-1.04785 - 2.52973i) q^{91} +(26.0036 - 62.7782i) q^{93} -85.8978i q^{95} +66.9192 q^{97} +(-86.3841 - 35.7815i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 28 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9	\( 28 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + 4 q^{11} - 4 q^{13} + 8 q^{15} + 4 q^{19} - 4 q^{21} + 68 q^{23} - 4 q^{25} + 100 q^{27} - 4 q^{29} - 8 q^{33} - 92 q^{35} - 4 q^{37} - 188 q^{39} - 4 q^{41} - 92 q^{43} - 40 q^{45} + 8 q^{47} - 224 q^{51} - 164 q^{53} - 252 q^{55} - 4 q^{57} - 124 q^{59} - 68 q^{61} - 8 q^{65} + 164 q^{67} + 188 q^{69} + 260 q^{71} - 4 q^{73} + 488 q^{75} + 220 q^{77} + 520 q^{79} + 484 q^{83} + 96 q^{85} + 452 q^{87} - 4 q^{89} + 196 q^{91} + 32 q^{93} - 8 q^{97} - 216 q^{99}+O(q^{100}) \) 28 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9 + 4 * q^11 - 4 * q^13 + 8 * q^15 + 4 * q^19 - 4 * q^21 + 68 * q^23 - 4 * q^25 + 100 * q^27 - 4 * q^29 - 8 * q^33 - 92 * q^35 - 4 * q^37 - 188 * q^39 - 4 * q^41 - 92 * q^43 - 40 * q^45 + 8 * q^47 - 224 * q^51 - 164 * q^53 - 252 * q^55 - 4 * q^57 - 124 * q^59 - 68 * q^61 - 8 * q^65 + 164 * q^67 + 188 * q^69 + 260 * q^71 - 4 * q^73 + 488 * q^75 + 220 * q^77 + 520 * q^79 + 484 * q^83 + 96 * q^85 + 452 * q^87 - 4 * q^89 + 196 * q^91 + 32 * q^93 - 8 * q^97 - 216 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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